# A generalisation of Mahler measure and its application in algebraic dynamical systems

Acta Arithmetica (1999)

- Volume: 88, Issue: 1, page 15-29
- ISSN: 0065-1036

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topManfred Einsiedler. "A generalisation of Mahler measure and its application in algebraic dynamical systems." Acta Arithmetica 88.1 (1999): 15-29. <http://eudml.org/doc/207228>.

@article{ManfredEinsiedler1999,

abstract = {We prove a generalisation of the entropy formula for certain algebraic $ℤ^d$-actions given in [2] and [4]. This formula expresses the entropy as the logarithm of the Mahler measure of a Laurent polynomial in d variables with integral coefficients. We replace the rational integers by the integers in a number field and examine the entropy of the corresponding dynamical system.},

author = {Manfred Einsiedler},

journal = {Acta Arithmetica},

keywords = {Mahler measure; topological entropy; dynamical system},

language = {eng},

number = {1},

pages = {15-29},

title = {A generalisation of Mahler measure and its application in algebraic dynamical systems},

url = {http://eudml.org/doc/207228},

volume = {88},

year = {1999},

}

TY - JOUR

AU - Manfred Einsiedler

TI - A generalisation of Mahler measure and its application in algebraic dynamical systems

JO - Acta Arithmetica

PY - 1999

VL - 88

IS - 1

SP - 15

EP - 29

AB - We prove a generalisation of the entropy formula for certain algebraic $ℤ^d$-actions given in [2] and [4]. This formula expresses the entropy as the logarithm of the Mahler measure of a Laurent polynomial in d variables with integral coefficients. We replace the rational integers by the integers in a number field and examine the entropy of the corresponding dynamical system.

LA - eng

KW - Mahler measure; topological entropy; dynamical system

UR - http://eudml.org/doc/207228

ER -

## References

top- [1] D. Hilbert, Gesammelte Abhandlungen, Bd. I, Springer, Berlin, 1932.
- [2] D. A. Lind, K. Schmidt and T. Ward, Mahler measure and entropy for commuting automorphisms of compact groups, Invent. Math. 101 (1990), 593-629. Zbl0774.22002
- [3] J. Neukirch, Algebraische Zahlentheorie, Springer, Berlin, 1992.
- [4] K. Schmidt, Dynamical Systems of Algebraic Origin, Birkhäuser, 1995. Zbl0833.28001